Average Error: 0.0 → 0.0
Time: 20.9s
Precision: 64
\[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]
↓
\[\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]
\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)
↓
\left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5
double f(double re, double im) {
        double r317150 = 0.5;
        double r317151 = re;
        double r317152 = sin(r317151);
        double r317153 = r317150 * r317152;
        double r317154 = 0.0;
        double r317155 = im;
        double r317156 = r317154 - r317155;
        double r317157 = exp(r317156);
        double r317158 = exp(r317155);
        double r317159 = r317157 + r317158;
        double r317160 = r317153 * r317159;
        return r317160;
}
↓
double f(double re, double im) {
        double r317161 = im;
        double r317162 = exp(r317161);
        double r317163 = re;
        double r317164 = sin(r317163);
        double r317165 = r317162 * r317164;
        double r317166 = r317164 / r317162;
        double r317167 = r317165 + r317166;
        double r317168 = 0.5;
        double r317169 = r317167 * r317168;
        return r317169;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(0.5 \cdot \sin re\right) \cdot \left(e^{0 - im} + e^{im}\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{0.5 \cdot (\left(\sin re\right) \cdot \left(e^{im}\right) + \left(\frac{\sin re}{e^{im}}\right))_*}\]
  3. Using strategy rm

  4. Applied fma-udef0.0

    \[\leadsto 0.5 \cdot \color{blue}{\left(\sin re \cdot e^{im} + \frac{\sin re}{e^{im}}\right)}\]

  5. Final simplification0.0

    \[\leadsto \left(e^{im} \cdot \sin re + \frac{\sin re}{e^{im}}\right) \cdot 0.5\]

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (re im)
  :name "math.sin on complex, real part"
  (* (* 0.5 (sin re)) (+ (exp (- 0 im)) (exp im))))